380 APPLIED MECHANICS 
is equal to p, the coefficient of sliding friction between the teeth. The 
driving force on the tooth of the lower wheel is now along the line dae, 
and the angle of obliquity 
of action is a+ ¢. 
If bisa point of con- 
tact between a pair of 
teeth during recess, PB is 
the angle of obliquity of 
action at b when friction is 
neglected. When friction 
is considered, the angle of 
obliquity of action at b is 
obviously B — ¢. 
The effect of friction is 
to increase the obliquity of Pies 
action during approach, and to diminish it during recess. Consequently 
friction is more objectionable during approach than during recess, 
The effect of friction in altering the direction of the pressure between 
a pair of teeth in contact may be better understood by reference to 
Fig. 581. mand 7 are portions 
of a pair of teeth in contact, 
and the arrows show the direc- 
tion of sliding of the one tooth 
on the other. R is the reaction 
of m on m, and T is the reaction 
of monn. T is of course equal 
and opposite to R. The left- 
hand portion of Fig. 581 shows 
the conditions during approach, 
while the right-hand portion 
shows the conditions during recess, m being on the driver and m on 
the follower. 
Referring further to Fig. 580, since the effect of friction is to divert 
the line of pressure between the teeth from the pitch point P, it is 
evident that during approach the length of the perpendicular from the 
centre of the driver to the line of pressure is diminished, and for a given 
turning moment on the driver at any instant the pressure on the teeth 
is increased by the action of the friction. During recess, however, the 
Follower. 
Fig. 581. 
™ 
‘length of the perpendicular from the centre of the driver to the line ~ 
of pressure is increased, and for a given turning moment on the driver 
at any instant the pressure on the teeth is diminished by the action 
of the friction. Hence friction is more injurious during approach than 
during recess. 
Friction does not affect the accuracy of the working of the teeth so 
far as velocity ratio at any instant is concerned. 
325. Involute Teeth.—Although the involute of a circle is a 
particular case of the epicycloid, being the epicycloid when the rolling 
circle is of infinite diameter, involute teeth are not considered as a 
special case of cycloidal teeth, because the involutes used are not 
involutes of the pitch circles, but are involutes of smaller circles, called 
the base circles. 
